Composite materials made from wood or other cellulose fibers or particles in combination with polymers such as polyethylene, polypropylene, and polyvinyl chloride have gathered increasing interest in recent years. Such “wood-polymer composites” have attracted attention due to the possibility of achieving products having the wood tone appearance of natural lumber combined with the durability of plastics. Inexpensive sources of plastics, such as from recycling operations, may provide additional advantages in terms of cost. However, one challenge is to provide composites having good physical properties relating to strength and toughness. Thus, there is commercial interest in compositions containing polymers and cellulose fibers or particles, particularly those exhibiting good physical properties.